Being a deadly disease, breast cancer provides higher global mortality among women. The challenge in employing ultrasound imaging for breast cancer diagnosis lies in the segmentation part. Thus, the work intends to segment the breast cancer ultrasound images using the deep learning approach. The U-shaped convolution neural network, U-Net, has become popular and efficient for biomedical image segmentation. Specifically, the paper proposes an improved version, SKMAT-U-Net, where a selective kernel (SK) utilizes an attention mechanism to adjust the receptive fields of the network and combine feature maps extricated with dilated and standard convolution operations. Next, based on the conventional cross-entropy loss function, four attention loss functions are integrated to form the Mixed Attention Loss Function (MAT) based U-Net. Thus, the SKMAT-U-Net model is proposed to segment the lesions effectively in breast ultrasound images. The results obtained indicated that the proposed U-Net model provides a better Dice score (0.929) than others.